Table 3 ARL and SDRL comparison of proposed and competing charts at n = 5.
ARL0 = 100 | ARL0 = 370 | ARL0 = 500 | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AEWMA_II | AEWMA_III | AEWMA_II | AEWMA_III | AEWMA_II | AEWMA_III | ||||||||||||||
h | 0.0945 | 0.1645 | 0.2065 | 0.2071 | 0.2341 | 0.2561 | 0.1795 | 0.2565 | 0.2985 | 0.2733 | 0.3054 | 0.3301 | 0.1977 | 0.2729 | 0.3149 | 0.287 | 0.3201 | 0.3463 | |
δ | ψ | 0.10 | 0.15 | 0.20 | 0.10 | 0.15 | 0.20 | 0.10 | 0.15 | 0.20 | 0.10 | 0.15 | 0.20 | 0.10 | 0.15 | 0.20 | 0.10 | 0.15 | 0.20 |
0.00 | ARL | 99.41 | 101.13 | 102.37 | 99.65 | 99.28 | 100.85 | 371.85 | 371.08 | 373.22 | 371.08 | 369.76 | 369.93 | 501.29 | 495.95 | 500.01 | 501.52 | 500.98 | 498.78 |
SDRL | 165.29 | 123.66 | 105.82 | 120.83 | 108.66 | 104.28 | 458.97 | 387.12 | 377.95 | 404.54 | 392.33 | 380.00 | 600.84 | 516.91 | 495.81 | 544.64 | 524.52 | 521.36 | |
0.25 | ARL | 7.61 | 10.79 | 12.84 | 10.75 | 11.87 | 12.65 | 13.32 | 18.24 | 21.04 | 16.22 | 18.50 | 19.49 | 14.80 | 19.79 | 23.21 | 17.99 | 20.44 | 22.40 |
SDRL | 9.09 | 10.01 | 9.74 | 9.35 | 9.63 | 9.83 | 12.95 | 13.63 | 13.54 | 13.69 | 14.74 | 14.94 | 13.68 | 14.14 | 14.34 | 14.85 | 16.22 | 17.30 | |
0.50 | ARL | 2.79 | 4.01 | 4.92 | 3.81 | 4.24 | 4.54 | 4.36 | 6.13 | 7.38 | 5.02 | 5.60 | 6.07 | 4.86 | 6.73 | 8.05 | 5.27 | 5.89 | 6.46 |
SDRL | 2.04 | 2.77 | 3.16 | 2.69 | 2.92 | 3.07 | 2.97 | 3.90 | 4.44 | 3.52 | 3.89 | 4.19 | 3.14 | 4.18 | 4.79 | 3.66 | 4.07 | 4.51 | |
0.75 | ARL | 1.76 | 2.30 | 2.70 | 2.19 | 2.38 | 2.54 | 2.42 | 3.13 | 3.67 | 2.65 | 2.83 | 2.99 | 2.69 | 3.37 | 3.84 | 2.76 | 2.96 | 3.13 |
SDRL | 0.96 | 1.49 | 1.70 | 1.30 | 1.41 | 1.50 | 1.54 | 2.08 | 2.34 | 1.60 | 1.79 | 1.91 | 1.69 | 2.23 | 2.44 | 1.70 | 1.93 | 2.01 | |
1.00 | ARL | 1.35 | 1.54 | 1.78 | 1.55 | 1.64 | 1.72 | 1.63 | 1.90 | 2.18 | 1.76 | 1.82 | 1.90 | 1.74 | 1.98 | 2.31 | 1.78 | 1.87 | 1.92 |
SDRL | 0.60 | 0.86 | 0.99 | 0.77 | 0.82 | 0.89 | 0.92 | 1.17 | 1.24 | 0.94 | 1.03 | 1.10 | 0.98 | 1.19 | 1.29 | 0.98 | 1.08 | 1.15 | |
1.50 | ARL | 1.05 | 1.07 | 1.15 | 1.09 | 1.12 | 1.13 | 1.09 | 1.15 | 1.28 | 1.14 | 1.14 | 1.15 | 1.13 | 1.20 | 1.32 | 1.15 | 1.14 | 1.16 |
SDRL | 0.21 | 0.27 | 0.37 | 0.30 | 0.35 | 0.36 | 0.30 | 0.40 | 0.50 | 0.37 | 0.39 | 0.40 | 0.36 | 0.44 | 0.52 | 0.39 | 0.38 | 0.42 | |
2.00 | ARL | 1.00 | 1.00 | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 | 1.02 | 1.04 | 1.01 | 1.01 | 1.01 | 1.01 | 1.02 | 1.05 | 1.01 | 1.01 | 1.01 |
SDRL | 0.05 | 0.06 | 0.11 | 0.10 | 0.11 | 0.11 | 0.08 | 0.13 | 0.19 | 0.11 | 0.12 | 0.12 | 0.10 | 0.15 | 0.22 | 0.12 | 0.11 | 0.12 | |
2.50 | ARL | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
SDRL | 0.01 | 0.01 | 0.02 | 0.01 | 0.02 | 0.02 | 0.02 | 0.03 | 0.04 | 0.01 | 0.02 | 0.03 | 0.02 | 0.03 | 0.06 | 0.02 | 0.02 | 0.02 | |
3.00 | ARL | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
SDRL | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
3.50 | ARL | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
SDRL | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
4.00 | ARL | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
SDRL | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
5.00 | ARL | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
SDRL | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
6.00 | ARL | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
SDRL | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
